A328559 - OEIS

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A328559

Numbers m that are neither arithmetic (A003601) nor squares (A000290).

2, 8, 10, 12, 18, 24, 26, 28, 32, 34, 40, 48, 50, 52, 58, 63, 72, 74, 75, 76, 80, 82, 84, 88, 90, 98, 104, 106, 108, 112, 117, 120, 122, 124, 128, 130, 136, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 180, 192, 194, 200, 202, 208, 216, 218, 226

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OFFSET

1,1

COMMENTS

Numbers m such that neither the arithmetic mean of the divisors of m nor the geometric mean of the divisors of m is an integer.

Numbers m such that neither A(m) = A000203(m) / A000005(m) nor G(m) = sqrt(m) is an integer.

Corresponding values of A(m): 3/2, 15/4, 9/2, 14/3, 13/2, 15/2, 21/2, 28/3, 21/2, 27/2, 45/4, 62/5, 31/2, 49/3, 45/2, ...

Corresponding values of G(m): sqrt(2), sqrt(8), sqrt(10), sqrt(12), sqrt(18), sqrt(24), sqrt(26), sqrt(28), sqrt(32), ...

LINKS

Table of n, a(n) for n=1..58.

MATHEMATICA

Select[Range[230], !IntegerQ@Sqrt[#] && !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Nov 01 2019 *)

PROG

(Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(m))]

CROSSREFS

Cf. A000005, A000203, A000290, A003601, A328557, A328558.

Sequence in context: A297999 A287088 A296342 * A328954 A343500 A176969

Adjacent sequences: A328556 A328557 A328558 * A328560 A328561 A328562

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Oct 31 2019

STATUS

approved